find the minimum of  f(x) = 2x^2 - 4x + 3

4 Answers | Add Yours

kjcdb8er's profile pic

kjcdb8er | Teacher | (Level 1) Associate Educator

Posted on

Find the minimum by taking the derivitive of the function and setting it to zero.

Use the power rule which states: d/dx [x^n] = n*x^(n-1)

f(x) = 2x^2 - 4x^1 + 3

f'(x) = 4x -4

Now set to zero

4x - 4 = 0

x = 1

minimum is at f(1) = 2 - 4 + 3 = 1 , or the point (1,1)

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

f(x) = 2x^2 - 4x + 3

First we need to determine f'(x)

f'(x) = 4x - 4

Now we need to find the critical values for f(x) which is f'(x)'s zero.

4x - 4 = 0

==> 4x = 4

==> x= 1

Then f'(x) has a minimmum values at x= 1

==> f(1) = 2(1) - 4(1) + 3

              = 2 - 4 + 3

              = 1

Then f has a minimmum value at (1, 1)

 

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The function f(x) = 2x^2 - 4x + 3 has a graph that s a parabola opening upwards.

The lowest point of the graph is the value where f(x) is minimum. This can be determined by writing the equation in the vertex form. If the vertex is at (h, k) the vertex form is y = a(x - h)^2 + k. The vertex is the minimum point.

f(x) = 2x^2 - 4x + 3

= 2x^2 - 4x + 2 + 1

= 2(x^2 - 2x + 1) + 1

= 2*(x - 1)^2 + 1

The vertex is (1, 1)

The minimum value of the function f(x) = 2x^2 - 4x + 3 is 1.

phucnguyen08's profile pic

phucnguyen08 | Student, College Freshman | (Level 1) Honors

Posted on

f(x)=2(x^2-2x+1)+1=2(x-1)^2+1

We have 2(x-1)^2>=0

so  f(x)=2(x-1)^2+1>=1

f(x) minimum=1 when x=1

We’ve answered 318,911 questions. We can answer yours, too.

Ask a question